Question

How do you solve `6^x=13`?

Answer 1

`x≈1.432" to 3 decimal places"`

Explanation:

Using the `color(blue)"law of logarithms"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(loga^n=nloga)color(white)(2/2)|)))`

`6^x=13`

Take the ln ( natural log ) of both sides.

`rArrln6^x=ln13`

`rArrxln6=ln13`

`rArrx=ln13/ln6≈1.432" to 3 decimal places"`